I've used silver maple before just like you are. be sure to seal the back so it doesn't check as it dries. In my experience, after reducing to near-bow dimensions, take it inside and put it on a curtainrod above a register, or a few feet above a baseboard heater for a couple weeks. Then flip it over for another couple, then you're good to go. I left mine on the back of a couch above a baseboard heater for a total of four weeks, and it was dry enough to continue. Haven't had a problem with it.
btw, some indians used to just build the bow green when they were in a pinch. It usually got some pretty wicked set, but it still worked!
You can take it to floor tiller stage, then clamp it in a reflex or reflex/deflex form while it dries, and it'll take on the shape (if you're into that sort of thing)